Motivation and definition of the inverse of a matrix
Notation for matrix entries, diagonal matrix, square matrix, identity matrix, and zero matrix.
The definition of matrix inverse is motivated by considering multiplicative inverse. The identity matrix and matrix inverse are defined.
In this section we specialize further and consider matrices with equal numbers of rows and columns, which when considered as coefficient matrices lead to systems with equal numbers of equations and variables. We will see in the second half of the course (Chapter D, Chapter E, Chapter LT, Chapter R) that these matrices are especially important.